I added a blur effect svg to my HTML(text/html):
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#svgBlur is a relative URL. It is converted to an absolute URL by prepending the name of the file it is in so
filter: url("#svgBlur");
in your case is really just a shorthand for
filter: url("stylesheet.css#svgBlur");
Which doesn't point to anything.
You need to put the name of the html file in the URL
filter: url("yourhtmlfile.html#svgBlur");
will work. And that's why it works when it's in the html file of course as the prepended filename points to the right place in that case.